Ever practical, the Roman liturgy provides for a special case in which a person has very suddenly fallen into deathly illness or a life-threatening injury. Provisions for the continuous rite are as follows:
30 For special cases, when sudden illness or some other cause has unexpectedly placed one of the faithful in proximate danger of death, a continuous rite is provided by which the sick person may be given the sacraments of penance, anointing, and the eucharist as viaticum in a single celebration.
The rite lists priorities: confession, then viaticum, and if time permits, anointing:
If death is imminent and there is not enough time to celebrate the three sacraments in the manner already described, the sick person should be given an opportunity to make a sacramental confession, even if it has to be a generic confession. After this, the person should be given viaticum, since all the faithful are bound to receive this sacrament if they are in danger of death. Then, if there is sufficient time, the sick person should be anointed.
Note the “generic” confession, which I assume would be a form like the Confiteor. If the person cannot ingest the Eucharistic elements, then anointing should follow penance:
The sick person who, because of the nature of the illness, cannot receive communion should be anointed.
You do realize that if time permits, an unconfirmed Catholic may be confirmed by the pastor. In an emergency, any priest may confirm. This is sometimes overlooked by a few priests who give pastoral care to seriously ill children.
31 If the sick person is to be strengthened by the sacrament of confirmation, nos. 238, 246, 276, 290, and 291 of this ritual should be consulted.
In danger of death, provided the bishop is not easily available or is lawfully impeded, the law gives the faculty to confirm to the following: pastors and parochial vicars; in their absence, associate pastors; priests who are in charge of special parishes lawfully established, administrators, substitute priests, and assistant priests (coadjutors); in the absence of all of the preceding, any priest who is not under censure or canonical penalty. (See Roman Pontifical, Rite of Confirmation, Introduction, no. 7c.)
I suspect that among parents, confirmation is rarely requested for a seriously ill child. But speaking as a parent, I’d want every spiritual advantage I could help muster for her.